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Ultraviolet stability in Euclidean scalar field theories

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Abstract

We develop a technique for reducing the problem of the ultraviolet divergences and their removal to a free field problem. This work is an example of a problem to which a rather general method can be applied. It can be thought as an attempt towards a rigorous version (in 2 or 3 space-time dimensions) of the analysis of the structure of the functional integrals developed in [9], the underlying mechanism being essentially the same as in [11,3].

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References

  1. Nelson, E.: A quartic interaction in two dimensions. In: Mathematical theory of elementary particles (eds. R. Goodman, I. Segal). Cambridge: MIT Press 1966

    Google Scholar 

  2. Benfatto, G., Cassandro, M., Gallavotti, G., Nicoló, F., Olivieri, E., Presutti, E., Scacciatelli, E.: Commun. Math. Phys.59, 143 (1978); Related works are: Gallavotti, G.: Memorie dell'Accademia dei LinceiXV, 23 (1978); Gallavotti, G.: Ann. Matematica Pura Appl.CXX, 1–23 (1979)

    Google Scholar 

  3. Guerra, F.: Phys. Rev. Lett.28, 1213–1215 (1972)

    Google Scholar 

  4. Glimm, J., Jaffe, A.: Fortschr. Physik21, 327–376 (1973)

    Google Scholar 

  5. Glimm, J., Jaffe, A., Spencer, T.: The particle structure of the weakly coupledP(ϕ)2 model and other applications. In: Lecture Notes in Physics, Vol. 25 (eds. G. Velo, A. Wightman). Berlin, Heidelberg, New York: Springer 1973

    Google Scholar 

  6. Feldman, J.: Commun. Math. Phys.37, 93–120 (1974)

    Google Scholar 

  7. Magnen, J., Seneor, R.: Ann. Inst. Henri Poincaré24, 95–159 (1976)

    Google Scholar 

  8. Magnen, J.: Thesis

  9. Feldman, J., Osterwalder, K.: Ann. Phys.97, 80–135 (1976)

    Google Scholar 

  10. Dobrushin, R.L., Tirozzi, B.: Commun. Math. Phys.54, 173–192 (1977)

    Google Scholar 

  11. Ruelle, D.: Commun Math. Phys.18, 127–159 (1970)

    Google Scholar 

  12. Ruelle, D.: Commun. Math. Phys.50, 189–194 (1976)

    Google Scholar 

  13. Dinaburg, R., Sinai, Ya.G.: To appear

  14. Simon, B.: TheP(ϕ)2 euclidean quantum field theory. Princeton: Princeton University Press 1974

    Google Scholar 

  15. Velo, G., Wightman, A.: Lecture Notes in Physics, Vol. 25. Berlin, Heidelberg, New York: Springer 1978

    Google Scholar 

  16. Benfatto, G., Gallavotti, G., Nicolo, F.: Elliptic equations and gaussian processes. Preprint IHES (1979). See also [2]

  17. Wilson, K.: Phys. Rev. B4, 3174–3183 and 3184–3205 (1971)

    Google Scholar 

  18. Pitt, L.: Arch. Rat. Mech. Anal.43, 367–391 (1971)

    Google Scholar 

  19. Glimm, J.: Commun. Math. Phys.10, 1–47 (1968)

    Google Scholar 

  20. Glimm, J., Jaffe, A.: Fortschr. der Physik21, 327–376 (1973)

    Google Scholar 

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Authors and Affiliations

  1. Istituti di Matematica e Fisica dell'Università, Rome, Italy

    G. Benfatto, M. Cassandro, G. Gallavotti, F. Nicoló, E. Olivieri, E. Presutti & E. Scacciatelli

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  1. G. Benfatto
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  2. M. Cassandro
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  3. G. Gallavotti
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  4. F. Nicoló
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  5. E. Olivieri
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  6. E. Presutti
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  7. E. Scacciatelli
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Additional information

Communicated by K. Osterwalder

Supported by IHES, through financial support from the “Stiftung Volkswagenwerk”

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Benfatto, G., Cassandro, M., Gallavotti, G. et al. Ultraviolet stability in Euclidean scalar field theories. Commun.Math. Phys. 71, 95–130 (1980). https://doi.org/10.1007/BF01197916

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  • DOI: https://doi.org/10.1007/BF01197916

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